<![CDATA[Background: There are diverse beliefs regarding the nature of mathematics, which directly influence the teaching and learning approaches adopted in mathematics education. These beliefs range from mathematics being a collection of facts, rules, and skills, to viewing it as a dynamic and ever-evolving discipline.Aim: This study investigates the beliefs of mathematics student teachers external supervisors regarding the nature of mathematics, learning mathematics, mathematics achievement, and their preparedness for teaching mathematics within an Open Distance e-Learning (ODeL) environment to address challenges and improve the effectiveness of Teaching Practice (TP) supervision.Method: A quantitative survey design was employed, utilizing a structured questionnaire adapted from the Firstmath Project. Data were collected from 43 respondents out of a population of 76 mathematics student teachers external supervisors, selected through random sampling across six provinces in South Africa. The analysis framework was guided by Ernest, three conceptions of mathematics: problem-solving, Platonist, and Instrumental views. Descriptive statistics were used to analyze the data.Results: The findings revealed a significant gap in external supervisors understanding of the mathematics classroom as a dynamic environment for teaching and learning. Many supervisors lacked exposure to contemporary pedagogical strategies tailored for the ODeL context.Conclusion: The study recommends the implementation of developmental programs aimed at equipping mathematics external supervisors with innovative approaches to teaching and learning mathematics. Such initiatives would enhance their readiness to support student teachers effectively in an ODeL environment.]]>
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